Don't Know the Chords? Start on Beat 2
At a Chicago Harmonica Masterclass Workshop (I believe in 2005) David Waldman shared a cool tip in regards to phrasing like Little Walter. He said, "If you want to emulate Little Walter's phrasing, start your licks on beat 2." He then played with the guitarist and improvised with this in mind, and sure enough, all of us instructors (Joe Filisko, Dennis Gruenling and Scott Dirks) nodded our heads in agreement... it sounded like what Walter would do. I experimented with this concept after the workshop and it's now a tool I use in my improvising from time to time.
Besides being a cool phrasing tool, I've found it to be the best way to improvise to a song I've never played to before in live performance that has a non-12 Bar Blues chord progression.
The idea is simple...
Instead of guessing what a chord is AS it changes, I rest on beat 1, letting the chord change first. Hearing the chord first allows me to identify the chord and play something that's musically appropriate on beat 2. The end result is not only a more rhythmically hip way of playing, it decreases my error rate based on guessing what the chord is probably going to be.